# Video Lectures

We argue that quantization, a mathematical model of the quantum classical correspondence, gives rise to approximate unitary representations of symplectomorphism groups. As an application, we get an obstruction to symplectic action of Lubotzky...

Bernstein's theorem (also known as the Bernstein-Khovanskii-Kushnirenko theorem) gives a bound on the number of nonzero solutions of a polynomial system of equations in terms of the mixed volume of its Newton polytopes. In this talk, we will give...

In 2017 Lucio Galeati understood that a suitable scaling limit of certain hyperbolic PDEs with noise may lead to deterministic parabolic equations. Since then, in collaboration with Lucio and Dejun Luo, we have understood the phenomenon from several...

I revisit the basic statistical problem of estimating the mean of a real-valued distribution. I will introduce an estimator with the guarantee that "our estimator, on *any* distribution, is as accurate as the sample mean is for the Gaussian...

A classical construction in topology associates to a space X and prime p, a new "localized" space Xp whose homotopy and homology groups are obtained from those of X by inverting p. In this talk, I will discuss a symplectic analog of this...

In this talk we will begin the discussion of the results in Bezrukavnikov's "On Two Geometric Realizations of the Affine Hecke algebra". We will put all the previous tools described in this series of talks together to construct the equivalence of...

Constraint metric approximation is about constructing an approximation of a group G, when the approximation is already given for a subgroup H. Similarly, constraint stability is about lifting a representation of a group G, when the lift is already...

Random sampling a subgraph of a graph is an important algorithmic technique. Solving some problems on the (smaller) subgraph is naturally faster, and can give either a useful approximate answer, or sometimes even give a result that can be quickly...